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J. Phys. Chem. C 2009, 113, 16668–16673
Molecular Dynamics for Surface Deposition of a Carbon Nanotube via Collision Leton C. Saha, Shabeer A. Mian, Hyojeong Kim, and Joonkyung Jang* Department of Nanomaterials Engineering, Pusan National UniVersity, Miryang 627-706, Republic of Korea ReceiVed: July 22, 2009; ReVised Manuscript ReceiVed: August 06, 2009
Our molecular dynamics simulation demonstrates that a carbon nanotube (CNT) colliding with a silicon surface forms a stable pillar structure. The CNT aligns vertically by reorienting its axis up to 75°, provided the tube end contacts the surface upon impact. The sputtering of silicon atoms and extensive fragmentation of the CNT occur during a high energy collision. The CNT relaxes its structure within 1 ps, but its energy relaxation takes almost 10 ps. 1. Introduction In many applications, it is desirable to deposit carbon nanotubes (CNTs) on a surface with controlled orientations. Examples include field emitters,1,2 field effect transistors,3 biological sensors,4 and computer logic circuits.5,6 Over the past years, there has been impressive progress in the surface deposition of CNTs. CNTs can be aligned on various surfaces using an electric field,7,8 acoustic waves,9 coordination chemistry,10 and directed assembly.11,12 Nevertheless, the molecular details underlying CNT deposition are not completely understood. Given that the structure of the CNT governs its electromechanical properties,13-15 we find it is important to understand how the structure of CNTs is affected by the presence of a surface. It is also of fundamental interest to determine the mechanism and dynamics for the surface binding of CNTs. Molecular dynamics (MD) simulations, which obviate the undesired complication and uncertainty in experiments, can provide clear insight into CNT deposition. Earlier simulation examined the deformation of a CNT under tensile strain along its axis16 or under collision with atoms.15 There have been studies on the mechanical stability of CNTs under impact with graphite,17 the coalescence of CNT with graphite,18 and nanoindentation using a CNT tip.19 However, there are no reports on the surface deposition of a CNT via collision, which is relevant to neutral beam or cold spray20 experiments. Herein, this study examined the structural and energetic dynamics of CNTs deposited via collision using MD simulations. Silicon was used as the surface, considering its importance as “the” substrate for functional devices. The results show that a CNT forms a stable pillar structure on the surface with or without deformation in its structure. Interestingly, the CNT shows a remarkable propensity to align straight, regardless of its initial orientation at impact. This is due to the dangling bonds of the C atoms at the tube end. The sputtering of Si atoms occurs for a high energy impact. The implications of these results are discussed in terms of the controlled surface deposition of a CNT. 2. Simulation Methods A (6,6) single-walled CNT colliding with either a Si (001) or (110) surface was simulated (Figure 1a). The CNT, made from 384 C atoms, was 3.8 nm long and 0.81 nm in diameter. The CNT was made to hit the surface with a projectile speed, Vp, in its axial direction (downward inclined arrow in Figure * Corresponding author. E-mail:
[email protected].
Figure 1. (a) Snapshot of the CNT colliding with a Si (110) surface. The CNT collides with a projectile speed Vpalong its axis (inclined arrow) and an incidence angle θ measured from the surface normal (Z direction). In this case, Vp ) 5 km/s and θ ) 45°. (b-e) Snapshots of CNTs forming permanent structures on the Si (110) after collision. In each panel, the surface atoms are drawn small to show the CNT structure clearly. Snapshots were taken at 9.5 ps after impact. θ is 30° (b), 45°(c), 60°(d), and 75°(e).
1a) and with an incidence angle θ measured from the surface normal (Z axis in Figure 1a). Five kilometers per second was chosen as the default Vp, which is almost 10 times higher than the typical speed in neutral clusters beams.20,21 However, it is two orders of magnitude smaller than that in an ion beam bombardment experiment (hundreds of km/s).22 Various projectile speeds ranging from 200 m/s to 15 km/s were also considered. The incidence angle was varied systematically as 0, 15, 30, 45, 60, and 75°. The initial separation of the CNT from the surface depends on the incidence angle and was varied
10.1021/jp906964b CCC: $40.75 2009 American Chemical Society Published on Web 08/26/2009
TRH: Surface Deposition of a CNT via Collision from 1.5 to 2.0 nm. The Si (110) and (001) surfaces were slabs of Si crystals with thicknesses of 5.52 and 5.84 nm, respectively. The atoms in the bottom layer of the slab were fixed throughout the entire simulation. Each surface has lateral dimensions of 15.82 nm × 5.84 nm and 14.53 nm × 5.84 nm for Si (110) and (001), respectively (note the lateral dimension of the surface is longer in the X direction than in the Y direction, see Figure 1a). The periodic boundary conditions23 were imposed to emulate a laterally infinite surface. The simulation box length along the Z direction was taken to be 50 nm in order to remove the periodicity in the Z direction. The total number of Si atoms was 26136 for both surfaces. The CNT and surface were equilibrated separately by running constant temperature (NVT) MD23 simulations near 300 K. To run our main simulation for the collision, we first selected three independent initial conditions out of equilibration. For each initial condition, the projectile velocity was added to the CNT, and its axis was oriented according to the given Vp and θ values. The collision of CNT was simulated using a constant energy (NVE) MD method.23 The force on each atom was calculated using the many-body Tersoff potential24 designed for covalent bonding systems containing C, Si, and their alloys. The van der Waals potential (such as the 12-6 potential) was not included but should be insignificant for a CNT moving with a high projectile speed. It is also found negligible in the previous simulation for an etching of Si surface with CNT tips.19 The MD trajectory was propagated using the velocity Verlet algorithm23 with a 0.2 fs time step. The impact time was defined as the time at which the CNT approaches within 0.178 nm of the surface (0.178 nm is the C-Si distance in a silicon carbide nanotube25). The MD simulation typically ran for 9.5 ps after impact. The above MD methods were implemented using the DLPOLY package.26 The internal energy of the CNT was analyzed as follows. At each time, the center of mass position and velocity were calculated. The internal position and velocity of the ith C atom, Vi (i ) 1, · · · , 384), were obtained by subtracting these b ri and b from the position and velocity of each C atom. The internal kinetic energy Kint is given by the sum over each atom as Kint ) (m/2)∑ib Vi2. The angular momentum b L and the moment of Vis. The inertia tensor I were also calculated from b ris and b rotational kinetic energy Krot and vibrational kinetic energy Kvib was calculated as Krot ) (1/2)(I-1b L) × b L and Kvib ) Kint - Krot (Krotwas negligible), respectively. Kvib is expressed as temperature units using the relation Tvib ) (2Kvib)/[(3 × 384 - 6)kB], where kB is the Boltzmann constant. Tvib becomes a true temperature if averaged over an ensemble of trajectories, and the potential function for the CNT vibration is harmonic. 3. Results and Discussion The analysis begins by showing the structural change in a CNT during its collision with a surface. Figure 1a shows the CNT (Vp ) 5 km/s and θ ) 45°) penetrating the surface at impact. The CNT later forms a stable structure on the surface with some deformation. Panels b-e of Figure 1 illustrate the final structure and orientation of the CNT for various incidence angles (snapshots taken at 9.5 ps after impact). The surface Si atoms are drawn small so that the CNT can be clearly seen. In all cases, the bottom of the CNT penetrates the surface and binds firmly with Si atoms. For θ < 60° (Figure 1b,c), the orientation of the CNT is close to its initial angle of incidence, and its structure remains straight along its axis. The structural deformation was localized around its bottom. Although not shown here, the structural distortion of the CNT was minimal for θ ) 0°.
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Figure 2. Distribution of the vibrational energy of a CNT. We calculated the distribution of the vibrational kinetic energy of each atom E for a CNT colliding with a Si (110) surface (at 9.5 ps after its impact on the surface). The distribution P(E) was plotted as a histogram. P(E) was normalized to give a unit area when integrated. (a) P(E) corresponding to Figure 1b, θ ) 30°. (b) P(E) for Figure 1e, θ ) 75°. P(E) for θ ) 75° is wider and shifted toward a higher energy.
As θ is increased to 60° (Figure 1d) and 75° (Figure 1e), the final orientation of the CNT deviates considerably from the incidence angle θ, and its axis bends by 90°or more. Note that the bending places the top end of the CNT in partial contact with the surface (for θ ) 75°, some Si atoms are dragged up from the surface). The structural deformation is extensive, ranging from the bottom to the waist of the CNT. This extensive deformation of CNT was also seen in the distribution of its internal kinetic energy Kint (Figure 2). Kint of each C atom for a high θ has a wide distribution, meaning more C atoms are energetically excited. Because of its mechanical strength, the CNT does not show significant fragmentation. This is in contrast with the massive fragmentation of the clusters of noble gas atoms27 or nitrogen28 in surface scattering. However, one or two atoms are occasionally separated from the CNT. Most of the detached atoms reside below the surface, but some of those atoms remain on the surface for θ ) 60° and 75°. The structural deformation of the CNT was quantified by calculating the root-mean-squared displacement (rmsd). The displacement of each C atom from its initial value was calculated. The average of the displacement squared was taken by summing over all of the C atoms. The rmsd is defined as the square root of that average. Because this rmsd depends on the translation and orientation of the CNT, we chose the minimum in the rmsd values obtained for various translations and orientations. The minimum was calculated using the method of Kabsh29 implemented in the Visual Molecular Dyanmics package.30 In Figure 3a, the rmsd was plotted as a function of the time elapsed after impact [θ ) 45° and Si (110)]. The rmsd at impact (time zero in Figure 3a) was nonzero because of the thermal fluctuations in the CNT structure from its initial structure. After impact, the rmsd increases rapidly and reached its maximum (about 0.33 nm), which can be called a structural excitation of the CNT. The time needed for this excitation is called the structural excitation time te (1.1 ps in this case). The excitation is followed by structural relaxation, in which the rmsd decreases and levels off to a finite value (0.14 nm) with some fluctuations with time. The relaxation was modeled by fitting the rmsd curve to an exponential function of time, t, a × exp(-
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Figure 3. (a) Change in structure and energy for a CNT in collision with a Si (110) surface. For θ ) 45°, the rmsd (lower solid line) was plotted as a function of the time elapsed after impact. The rmsd after its maximum is fitted to an exponential function of time (dotted line). Also plotted is the vibrational kinetic energy in units of temperature Tvib (upper solid line, refer to the right Y axis). (b) Time-dependent rmsd for various incidence angles; Si (001) surface. The rmsd versus time was plotted for θ ) 0 (9), 15 (O), 30 (2), 45 (0), 60 (b), and 75° (4). Each line is a collection of data points, and the symbols are drawn as a visual guide. The symbols for θ ) 0°, 15°, and 30° overlapped with those for θ ) 45°. (c) Time variation in Tvib for various incidence angles; Si (001) surface. Tvib is plotted for the same set of incidence angles with the same symbols as in Figure 3b.
t/τ) + b (shown as a dotted line in Figure 3a). The fitting parameter τ is called the structural relaxation time of the CNT (0.33 ps for this case). Another fitting parameter b (0.135 nm) is the asymptotic rmsd at long times and quantifies the permanent structural damage to the CNT. The dependency of τ and b on θ was investigated below. Also plotted in Figure 3a is the time variation of Tvib under the same conditions as in the rmsd curve (refer to the right Y axis). Tvib fluctuates more than the rmsd, presumably due to the absence of self-averaging as in the rmsd (averaging over C atoms). Because our MD simulation conserves energy, Tvib fluctuates even if the CNT is isolated (Tvib fluctuates between 300 and 415 K with time). Tvib happens to be 350 K at the impact. Shortly after impact, Tvib increases even faster than the rmsd and reaches a plateau lasting approximately 0.7 ps and increases again to its maximum (1800 K) within 1.5 ps. The excitation time for Tvib is longer than te because of this plateau. After excitation, Tvib decreases gradually, and this energy relaxation is much slower than structural relaxation. Therefore, we cannot see Tvib leveling off in Figure 3a. The rmsd was examined by varying the incidence angle θ and the surface. In Figure 3b, the time-dependent rmsd for Si (001) was plotted by changing θ to 0°, 15°, 30°, 45°, 60°, and 75°. The symbols for θ ) 0°, 15°, and 30° overlapped with those for 45° and are not clearly seen. Every rmsd curve initially increases to a maximum (excitation) and then decreases to a finite value (relaxation). Quantitatively, each curve differs in its values of te, b, and height of excitation. Overall, as θ increases, structural excitation becomes slower (increased te) and larger in magnitude (increased maximal height of rmsd) and b increases. Figure 3c shows Tvib for the same set of incidence angles as in Figure 3b. As in Figure 3a, Tvib initially becomes excited to its maximum and then relaxes gradually. The energy relaxation was not completed within 9.5 ps for all
Saha et al.
Figure 4. Long-time behavior of the relaxation in the vibrational kinetic energy Tvib. Tvib after its maximum is drawn for θ ) 0°and Si (110). Tvib at time t was fitted to an exponential function, a × exp(- t/τ) + b and was drawn as a solid line. Relaxation time τ obtained from the fit was 8.7 ps.
Figure 5. Incidence angle θ dependency of various dynamical and structural quantities. In all panels, 9 and b refer to data obtained for Si (110) and (001), respectively, and lines are drawn as a visual guide. All data points were calculated by averaging over three independent MD trajectories, and the error bars represent standard deviations. (a) Structural excitation time te versus θ. (b) Structural relaxation time τ versus θ. (c) Asymptotic rmsd b versus θ. (d) Penetration depth versus θ.
of the cases in Figure 3c. An increase in θ generally enhances Tvib, but the Tvib values for θ < 75° were similar in magnitude. In the case of θ ) 0°and Si (110), the MD simulation was extended to 30 ps. Tvib finally levels off as shown in Figure 4. The relaxation time for the vibrational energy was found to be 8.7 ps, which is 17 times longer than τ in Figure 3a, using a similar fit to the above. The incidence angle θ dependence of various dynamical and structural quantities was examined. All quantities for Si (110) and Si (001) in Figure 5 were averaged over three independent MD trajectories. The standard deviations are drawn as error bars. Figure 5a shows a plot of the structural excitation time te versus θ. The value for te increases with increasing θ, varying from 0.42 to 1.52 ps. As shown in Figure 1, an increase in θ increases the structural distortion of the CNT (Figure 1d,e). Broader distortion, which involves more atoms, takes more time than localized distortion for small θ values (Figure 1b,c). In contrast,
TRH: Surface Deposition of a CNT via Collision τ turns out to be independent of θ. For each θ value, the rmsd was fitted after the excitation as in Figure 3a. The average τ was plotted as a function of θ in Figure 5b. τ ranged from 0.28 to 0.84 ps, not showing a clear trend in its dependency on θ. The permanent structural change in the CNT was quantified as the asymptotic rmsd, b, and plotted as a function of θ (Figure 5c). b was obtained from the same fit used for τ. As θ changes from 0°to 45°, b remains relatively constant (approximately 0.1 nm), but its magnitude was increased 5 times as θ was increased to 60° and 75°. The error bar of b was also large for θ ) 60°and 75°, meaning the structural change is sensitive to the initial conditions of the CNT. In Figure 5d, the penetration depth of the CNT was plotted by changing θ. The penetration was as deep as 1.1 nm below the surface for θ ) 0°. The depth remained constant as θ was increased from 0° to 15° and 30°. With further increases in θ, the decreasing behavior of the depth was clear [down to 0.1 nm for θ ) 75°and Si (001)]. The reduced penetration depth for an increased θ value is attributed to a decrease in the projectile velocity along the direction perpendicular to the surface. Interestingly, all results in Figure 5 are quite independent of whether the surface is (110) or (001). CNTs were simulated with Vp ) 1 km/s, which is close to the typical speed in neutral beam experiments. In this case, irrespective of the incidence angle, the CNT structure remained undamaged throughout deposition. In the case of θ ) 0° for Si (110), the rmsd and penetration depth were 0.04 and 0.12 nm, respectively. This rmsd is almost identical to that for an isolated CNT, demonstrating that the structure of the CNT remains intact. Surprisingly, the final orientation of the CNT was always upright on the surface regardless of the θ value. Figure 6a shows five CNTs, which initially have different θ ) 0°, 15°, 30°, 45°, and 60° for the Si (110) surface. At or shortly after impact (each CNT has a different impact time, and Figure 6b is a snapshot taken at 1.29 ps), each CNT binds to the surface without changing its initial orientation. With time, the CNTs gradually reorient their axes toward the direction perpendicular to the surface. By 10 ps (Figure 6c), all the CNTs are aligned perpendicularly to the surface. Although not shown, it was confirmed that the CNT stands upright even for θ ) 75°. This result can be explained as follows. The binding of the CNT to the surface is largely due to the bonds formed between the C atoms at the bottom end of the CNT and surface Si atoms. In the case of θ ) 0°, the entire bottom end of the CNT touches the surface at impact and immediately makes bonds with the surface atoms to give an upright pillar structure. For a nonzero θ (inclined CNT), only a part of the bottom hits the surface initially. Once even a tiny piece of the bottom end binds to the surface, the remainder of the bottom gradually creates bonds with the surface atoms. This gradual bond-making process between the C and Si atoms is like the zipping of dangling bonds beginning near the C atoms already making bonds with the surface atoms at impact. The end result of such a zipping process is a CNT standing upright on the surface. Even if Vp is decreased to as low as 200 m/s, a stable CNT pillar forms on the surface for θ < 60°. However, for θ ) 60°or above, the CNT bounces from the surface after impact and later lies down on the surface. In this case, contact of the CNT bottom with the surface is limited in area (due to a large value of θ), and the impact speed of the CNT is not sufficient to create an initial bond between the CNT and surface. This suggests that a CNT can be aligned upright on a surface by controlling its orientation and speed of impact. In this case, the “sticky” bottom end of CNT hits the surface with sufficient speed to create an initial bond between the C and Si atoms.
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Figure 6. Simultaneous deposition of five CNTs with different θ values; Si (110) surface. (a) Initial snapshot of five CNTs with different θ values of 0° (middle), 15° (back left), 30° (front right), 45° (front left), and 60° (back right). All CNTs have Vp ) 1 km/s. (b) CNTs at or shortly after impact with the surface (snapshot taken at 1.29 ps). (c) CNTs aligned vertically on the surface (from left to right, CNTs with θ ) 15°, 45°, 0°, 60°, and 30°). Snapshot was taken at 10 ps.
One might argue that the carbon atoms on the side wall of the CNT interact with the surface through the van der Waals interaction. Such additional interaction might tend to make the CNT lie down on the surface instead of standing up. To confirm our results, we have included the LJ interaction between carbon and silicon atoms reported by Mao et al.31 An MD simulation including the LJ potential also shows the same standing up of a CNT as found in Figure 6, regardless of the incidence angle. Once the tube end of CNT contacts and bonds with the surface, the carbon atoms on the side wall are farther away from the surface than those located at the tube end. The nonpolar LJ interaction is short ranged compared to the electrostatic or dipolar interaction. The LJ interaction therefore does not make the carbon atoms on the wall interact with the surface. Extremely high Vp values of 10 and 15 km/s were considered as well. For θ ) 0°, the entire CNT was immersed inside the surface. Several C and Si atoms are separated from the CNT and surface, respectively. As θ increases, extensive fragmentation of the CNT occurs. In the case of Vp ) 15km/s and θ ) 75°, the CNT is completely shattered and scattered into the vacuum in forms of individual atoms and small clusters (Figure
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Saha et al. significant fragmentation of the CNT is found because of its mechanical strength. For incidence angles θ of 60°and above, the CNT bends its axis. The structural excitation of CNT requires
